101011 B to Ary – Easy Conversion Explained

The binary number 101011 converts to 43 in ary.

To explain, binary 101011 means 1×2^5 + 0×2^4 + 1×2^3 + 0×2^2 + 1×2^1 + 1×2^0, which equals 32 + 0 + 8 + 0 + 2 + 1 = 43. So, when translating from binary to an ary system (base 43), the decimal 43 corresponds directly to 10 in base 43.

Conversion Result

Conversion Formula

To convert from binary (base 2) to ary (base 43), first, change the binary to decimal. This involves summing each digit times 2 raised to its position, then converting that decimal into base 43. The formula: decimal = sum of (digit × 2^position). To go from decimal to ary, repeatedly divide by 43, recording remainders.

Example: binary 101011 to decimal: (1×2^5)+(0×2^4)+(1×2^3)+(0×2^2)+(1×2^1)+(1×2^0)= 43. Then, 43 divided by 43 is 1 with 0 remainder, so in base 43, it’s written as 10.

Conversion Example

• Binary 1101 to decimal: (1×2^3)+(1×2^2)+(0×2^1)+(1×2^0)=8+4+0+1=13.
• Decimal 13 to base 5: 13/5=2 remainder 3; 2/5=0 remainder 2. So, 13 in base 5 is 23.
• Binary 1001 to decimal: (1×2^3)+(0×2^2)+(0×2^1)+(1×2^0)=8+0+0+1=9.
• Decimal 9 to base 4: 9/4=2 remainder 1; 2/4=0 remainder 2; thus, 9 in base 4 is 21.
• Binary 1110 to decimal: 14; decimal 14 to base 7: 14/7=2 remainder 0; in base 7, 14 is 20.

Conversion Chart

This chart shows decimal values from 100986.0 to 101036.0 and their conversion into base 43. Read the table to find out how such values are recorded in base 43, where each number is broken into remainders after division by 43.

Related Conversion Questions

• How do I convert binary 101011 to hexadecimal?
• What is the decimal equivalent of binary 101011?
• How can I change 101011 from binary to base 10?
• What is the base 43 representation of binary 101011?
• How to convert binary 101011 to octal?
• What is the process for translating binary 101011 into a custom base system?
• Can I convert 101011 binary directly to base 50?

Conversion Definitions

b: A base system, where “b” indicates binary (base 2), a numbering system using only 0s and 1s, representing values through positional notation, where each digit’s value is determined by its position and the base.

ary: A numeral system with base 43, using digits 0-9 and letters A-G, representing numbers with each position indicating a power of 43, enabling compact notation of large numbers in that base.

Conversion FAQs

How is binary 101011 converted into decimal?

Binary 101011 is calculated by summing each digit times 2 raised to its position: 1×2^5 + 0×2^4 + 1×2^3 + 0×2^2 + 1×2^1 + 1×2^0, which equals 32 + 0 + 8 + 0 + 2 + 1 = 43.

Why does the decimal value 43 convert to 10 in base 43?

Because 43 divided by 43 equals 1 with a remainder 0, the base 43 number is recorded as 10, where the left digit represents the quotient and the right the remainder, similar to how decimal 10 is written as 10 in base 10.

What are the steps to convert decimal 43 into base 43?

Divide 43 by 43: quotient 1, remainder 0. Record the remainder (0). Since quotient is less than 43, it becomes the most significant digit. So, 43 in base 43 is 10, with 1 as the leading digit and 0 as the last.

Can I convert other binary numbers to base 43 using this method?

Absolutely, the process involves first converting the binary to decimal, then repeatedly dividing by 43 to get remainders, which form the digits of the number in base 43, read from last to first.

Is there an easier way to convert binary directly to base 43?

Usually, conversion involves two steps: binary to decimal, then decimal to base 43. Direct conversion would require complex algorithms, so the two-step method is recommended for clarity and accuracy.